Sharp bounds on the density, Green function and jumping function of subordinate killed BM (2004)
by
Renming Song
| Venue: | PROBAB. THEORY RELAT. FIELDS |
| Citations: | 15 - 12 self |
BibTeX
@MISC{Song04sharpbounds,
author = {Renming Song},
title = { Sharp bounds on the density, Green function and jumping function of subordinate killed BM },
year = {2004}
}
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Abstract
Subordination of a killed Brownian motion in a domain D ⊂ R d via an α/2-stable subordinator gives rise to a process Zt whose infinitesimal generator is −(−�|D) α/2, the fractional power of the negative Dirichlet Laplacian. In this paper we establish upper and lower estimates for the density, Green function and jumping function of Zt when D is either a bounded C 1,1 domain or an exterior C 1,1 domain. Our estimates are sharp in the sense that the upper and lower estimates differ only by a multiplicative constant.
